Badal systems are known and most usually encountered in testing of the human eye. Such a system is illustrated with respect to FIG. 1.
Referring to FIG. 1, a Badal lens B is placed in front of a human eye E. The Badal lens is positioned so that its focal point is coincident with the position of the eye to be tested. Although only one lens is here illustrated, the reader will understand that more than one lens is more typical of such systems.
The patient at eye E views an acuity target T through the Badal optics B, this target being positioned for towards and away movement 14 with respect to the patient along an optic axis O in what is usually referred to as the Badal space S on the opposite side of the Badal optics from the patient's eye.
The patient subjectively determines when the target T on the opposite side of the Badal lens is in focus. Thereafter the distance D of the object from the Badal optics is determined and related to the power of the patients eye. By relating this determined power of the patient eye to the emmetropic standard, the prescription required for the correction of the patient's vision is determined.
It is a characteristic of the Badal system that the target examined by the patient on the opposite side of the Badal optics does not change size. This phenomena can be understood in the diagram of the line 16. A second, fundamental, property of a Badal system is that the "effective power" generated in the focal plane of the Badal system is linearly related to the movement of the target T in the Badal space.
Specifically, since the Badal lens is one focal length from the eye of the patient, all light from the image of the patients eye is parallel at lines 16 once it passes through the Badal optics to the so-called Badal space on the opposite side of the Badal optics from the patients eye. Thus what the patient sees during the toward and away motion is the Badal object or target T moving into and out of focus--but always maintaining the same dimension.
The distance that the target moves with towards and away movement and comes into focus in the Badal space is a function of the power of the patients eye. Considering the case of light focusing on the eye of the patient at broken lines 18. In FIG. 1, an example is used of an emmetropic eye (the eye having "perfect" vision when the eye is in the "relaxed" state) focused to optical infinity. It can be understood that such focus will occur when the light incident to the eye from the Badal object is parallel. This light will be parallel when the target is at one Badal lens focal length from the emmetropic eye. Thus, for the emmetropic eye, all light from the target to the eye will be parallel--just as all light from the eye to the object will be parallel. For purposes of this analysis, the light can be said to come to focus at the retina along plane 22.
Considering the case of an eye with hypermetropia (farsighted), it will be understood that parallel light seen by the eye (in the so-called "relaxed" state) will focus behind the retina at plane 23. By converging the light seen by the eye, light can be brought into focus at the patient' retina.
In this case, target T is move slightly more than one focal length from the Badal optics B. Parallel light from the target T to the Badal optics B is refracted by the Badal lens to have slight convergence. This slight convergence coupled with the less than optimum convergence of the hypermetropic eye produces focus of the image of the target T on the patient's retina at plane 22.
Considering the case of an eye with myopia (nearsightedness), it will be understood that parallel light seen by the eye (in the so-called "relaxed" state) will focus in front of the retina at plane 24. By diverging the light seen by the eye, light can be brought into focus at the patient's retina at plane 22.
In this case, target T is moved slightly less than one focal length from the Badal optics B. Parallel light from the target T to the Badal optics B is refracted by the Badal lens to have slight divergence. This slight divergence coupled with the more than optimum convergence of the myopic eye produces focus of the image of the target T on the patient's retina at plane 22.
Those having skill in the optic arts will realize that the above explanations are over simplified. Taking the most commonly encountered case of astigmatism, it will be appreciated that the focus of the Badal optics must be broken down into components or "principal meridians". Since the introduction of these complications is fully understood in the art, the following disclosure will continue assuming for the most part focus of the eye in a single principal meridian. The incorporation of additional meridian measurements and their combination to prescribe the astigmatic eye will be for the most part assumed hereafter.
It will be realized from the above descriptions that all Badal systems described have relied upon a Badal object or target T moving with towards and away motion in the Badal space to effect either convergence or divergence for the correction of the other than emmetropic eye. What follows is a Badal system. However, measurement is not made by movement of an object towards and away from Badal optics. Instead, measurement is made by sampling the optical system under test at discrete points and measuring excursion in a plane normal to the axis of the Badal system.
Regarding the keratometer disclosed herein, two types of kerotometric design principles are relevant. These are the Javal design principle and the Helmholtz design principle.
In the Helmholtz design principle, the incident light upon the cornea from an individual source is collimated at a fixed angle. The area sampled on the cornea is moved over the cornea. This movement continues until the light comes off the cornea at a fixed angle. It is this movement of the sample spot on the surface of the eye which is measured to measure the curvature of the eye.
In the Javal keratometer design principle, the incident light upon the cornea is directed to the same spot on the cornea. This light, however, is varied in angle until the sampled and reflected light comes off the cornea at a fixed angle from the fixed sample area on the cornea. The measurement of curvature is found from the position of the source angle.